which is equivalent to the following minimization problem [1]}, [2]}, [3]}
\(\inf _{u \in X, b \in Z}L_{HL}(u , b ):=D(u)+\frac{\mu }{2} \int _{\Omega }(b \cdot \frac{|\nabla u |^2}{\lambda }+b - \log (b ) -1)\mathrm {d}\sigma , \quad b >0.\) 
